Higher order theory for free vibration analysis of functionally graded material plates

In this paper, an analytical solution is developed to study the free vibration analysis of functionally graded material (FGM) plate without enforcing zero transverse shear stress conditions on the top and bottom surfaces of the plate using higher order displacement model. The material properties are assumed to be varied continuously through the thickness direction according to a simple power law distribution in terms of volume fraction of material constituents. The effective material properties are obtained by applying linear rule of mixtures. The derivation of equations of motion for higher order displacement model is obtained using principle of virtual work. The governing equations of FGM plate are established by applying energy principles and are solved by Navier’s method. The influence of side-to-thickness ratio, modulus ratio and aspect ratio on the non-dimensional natural frequencies is studied. The obtained numerical results are compared with the results available in the literature.